Factor completely, or state that the polynomial is prime.

Select the correct choice below and fill in any answer boxes within your choice.
A.
B. The polynomial is prime.

First, let’s factor out the greatest common factor from the expression . The greatest common factor is , so we can rewrite the polynomial as:

Now, the expression is a difference of squares, which can be further factored into:

So, the complete factorization is:

You can further understand that this polynomial is more than just the first factor you see—it’s a product of three factors, which gives you insight into its roots and x-intercepts.

For real-world application, polynomials like the one we just factored often appear in physics and engineering, especially in equations describing motion or systems. For instance, if you were analyzing the trajectory of a projectile, understanding how to factor polynomials will help you describe and predict its path because it reveals critical points where the object may change direction or speed!